what is 24x⁵+108 find the gcmf
Answer (1)
Greatest Common Monomial FactorHere's how to solve the problem:Step 1: Find the Greatest Common Factor (GCF) of the coefficientsThe coefficients are 24 and 108. Let's find their GCF.Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108The greatest common factor of 24 and 108 is 12.Step 2: Find the GCF of the variable termsThe variable term in the first part of the expression is x⁵. The second term, 108, has no variable term, so the GCF of the variable terms is just 1 (since x⁰ = 1).Step 3: Combine the GCF of the coefficients and the GCF of the variablesThe GCF of the coefficients is 12, and the GCF of the variable terms is 1. Therefore, the Greatest Common Monomial Factor (GCMF) is 12 × 1 = 1.Step 4: Factor the original expression using the GCMFNow, we factor out the GCMF (12) from the original expression:24x⁵ + 108 = 12(2x⁵ + 9)Final answer:The Greatest Common Monomial Factor (GCMF) is 12. The factored expression is 12(2x⁵ + 9).
